We will discuss questions surrounding automorphic L-functions, particularly Deligne’s conjecture about critical values of motivic L-functions. In particular, we study the adjoint L-function of U(2,1).

Hundley showed that a certain integral, involving an Eisenstein series on the exceptional group G_2, computes this L-function at unramified places. We discuss the computation of this integral at the archimedean place for quaternionic modular forms, and how this relates to Deligne's
conjecture.